A string is clamed at both the ends and it is vibrating in its $4^{\text {th }}$ harmonic. The equation of the stationary wave is $\mathrm{Y}=0.3 \sin (0.157 \mathrm{x}) \cos (200 \pi \mathrm{t})$. The length of the string is: (all quantities are in SI units)

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Waves & Sound

A string is clamed at both the ends and it is vibrating in its

4^{th}

harmonic. The equation of the stationary wave is

Y = 0.3 sin (0.157 x) cos (200 π t)

. The length of the string is: (all quantities are in SI units)

Answer: (A)

For a string clamped at both ends the

n

th harmonic fits

n

half-wavelengths into the length, so for the fourth harmonic

L = 4 \cdot \frac{λ}{2} = 2 λ

. Reading the wave number from

Y = 0.3 sin (0.157 x) cos (200 π t)

, we have

k = 0.157 = \frac{2 π}{λ}

, so

λ = \frac{2 π}{0.157} \approx 40

m. Hence

L = 2 λ = 80

JEE Main · 2019 · 09 Apr 2019 · Shift 1 · Single correct option